Feedback EDF Scheduling Exploiting Dynamic Voltage Scaling

Yifan Zhu and Frank Mueller

Department of Computer Science

Center for Embedded Systems Research

North Carolina State University

Overview

Motivation Background Feedback-DVS Example Experiments Summary

Motivation

Embedded systems w/ limited power supply DVS for real-time system

trade-off: energy saving vs. timing requirements lower CPU voltage/frequency deadline may miss

Task workloads change dynamically WCET overestimates actual execution time wide variation of execution times

• Longest vs. shortest times

Motivation

Prior DVS algorithms: lack adaptability to dynamic workloads.

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WCET Utilization

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c==50%WCET

c in [20%WCET, 80%WCET]

Real-world examples: graphics: 78% of WCET [Wegener,Mueller]; defense: 87%; automotive: 74%; benchmarks: 30-89%; image recognition: 85% [Wolf]

Look-ahead DVS [Pillai/ Shin]

Background

DVS: E ~ f V²

Hard real-time systems periodic, preemptive, independent tasks [Liu, Layland] jobs: periodically released instances of a task WCET: measured at full freq., w/o DVS most practical system: U << 1

Earliest-deadline-first (EDF) scheduling

, Ci=WCET, Pi=period

, = (0< 1) scaled by frequency

1i i

i

P

C

n

i i

i

P

C

1maxf

fk

Feedback-DVS Framework

V/F selector:

error c – Ca Ca = func(error)

Fig. Feedback-DVS Framework Maximum EDF schedule

determine slack in EDF schedule assumes: c = WCET

Voltage-Frequency Selector

1}{\},...,1{

1

kni i

i

k

k

P

C

P

C :

Greedy scheme: assign all idle time/slack to running task

Assuming all other tasks at the maximal freq. (speed) Capitalize on early completion of current task

early completion more slack for other tasks repeat scaling on next task

Task Splitting

T Ta + Tb Ta at freq. ( 0 100%); Tb at freq. 100% More aggressive:

• < uniform frequency w/o splitting Objective:

• T should finish before Tblower energy consumption

Solve for Ck = Ca+Cb (w/o slack) Ck+slack = Ca/ +Cb = Ca/(Ca+slack)

Tb

100%

f

tTa

Ca/ Cb

Slack Collection

Static and dynamic slack U<100% static slack Idle task: fills gap between actual U and 100% U Early completion dynamic slack Slack passing

Preemption handling Reserve future execution time for preempted task Avoid over-utilizing slack by high priority tasks Backward sweep reservation

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Example (w/o Feedback)

T1 T2 T3

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0 5 10 15

100%75%50%25%

T1={C=3,P=8,c=2} T2={C=3,P=10,c=2}T3={C=1,P=14,c=1} IdleT={C=1,P=4,c=0} Ca=50%WCET

I I T1 I T2

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Maximal Schedule (EDF with idle task)

Actual Schedule (w/o Feedback)

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f

f

t

t

We can do better!

Feedback Control

Scaling factor: =Ca/(Ca+slack) Feedback control: to adjust Ca

0<Ca<=WCET Objective:

Ca actual exec. time (c) But actual exec. time changes dynamically

high processing demands up to some point receding processing demands afterwards

PID Feedback control to improve adaptability to exec. time fluctuations

PID Feedback

Controlled variable: Ca Set point: c System error: = c – Ca When Ca c:

T = Ta, no Tb, entire task at low freq./speed PID: Proportional + Integral + Derivative

Proportional control:

Integral control:

Derivative control:

IW

jijI 1

1

ijK

DWD

DWjiij ,

PID

c

Ca +-

Ca

Feedback Example

0 5 10 15

0 3 5 6.5 10 15

T1={C=3,P=8,c=2} T2={C=3,P=10,c=2}T3={C=1,P=14,c=1} IdleT={C=1,P=4,c=0}

I T1 T2 T3

100%75%50%25%

I I T1 I T2

Maximal Schedule (EDF + idle task)100%75%50%25%

Actual Schedule without feedback100%75%50%25%

Actual Schedule with feedback (from the 1st hyperperiod) 480 485 490 495

Ca=2,s=2

f

f

f

t

t

t

Ca=1,s=2Ca=2,s=2

Algorithm Complexity

Task admission (offline): generate maximal schedule: O(N)

• N = # jobs in hyperperiod Scheduling point (online):

O(n), n = # tasks Task splitting overhead:

only paid when task does not complete within Ta• hardly even happens

Experiements

Frequency/Voltage levels [Puwelse et al.]: Parameters: 3 tasks, 10 tasks, Vary U: utilization=0.1~ 1.0 Feedback controller

DW=1, IW=10 Kp=0.9, I=0.08, D=0.1

Compare: Our feedback-DVS vs. Look-ahead DVS [Pillai/Shin]

Freq. Voltage

25% 2V

50% 3V

75% 4V

100% 5V

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WCET Utilization

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Our Feedback-DVS

Look-ahead RT-DVS

Result (1)

Task exec. time pattern 1: event-triggered activities,

often observed in interrupt-driven systems

c

job

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WCET Utilization

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Our feedback-DVS

Look-ahead RT-DVS

Result (2)

Task exec. time pattern 2: simulating computational

demands with slowly decaying tendency

c

job

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WCET Utilization

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Our Feedback-DVS

Look-ahead RT-DVS

Result (3)

Task exec. time pattern 3: periodic fluctuating activities

with peak computational demands

c

job

Varying Task Sets Property

10 tasks vs. 3 tasks Varying exec. time (baseline: pattern 1)

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WCET Utilization

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Ours,baseline=75%WCET

Ours, baseline=50%WCET

Ours, baseline=25%WCET

Look-ahead, baseline=75%WCET

Look-ahead, baseline=50%WCET

Look-ahead, baseline=25%WCET

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WCET Utilization

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10 tasks, ours

10 tasks, Look-ahead

3 tasks, ours

3 tasks, Look-ahead

Related Work

Feedback control real-time scheduling [C. Lu et. al.] DVS with feedback for multimedia systems [Z. Lu et. al.] Look-ahead DVS [Pillai/Shin] Exploit early completion of tasks [Aydin et. al.] Dual-frequency DVS, stochastic approach [Gruian] Non-preempt. Blocking, dual-speed DVS [Zhang et. al.]

Conclusion

Feedback-DVS for hard real-time systems more aggressive by task splitting more adaptive with feedback control

Not sensitive to particular workload characteristics O(n) online complexity Up to 29% more energy savings over prior workFuture Work Feedback analytical model Real-world architecture evaluation Systematic PID parameter tuning

Example (w/o Feedback)

T1 T2

0 5 10 15

100%75%50%25%

0 5 10 15

100%75%50%25%

T1={C=4,P=10,c=1} T2={C=4,P=14,c=1}T3={C=1,P=17,c=1} IdleT={C=1,P=4,c=0} Ca=50%WCET

T1I

Maximal Schedule (EDF with idle task)

Actual Schedule (w/o Feedback)

f

f

t

t

it will be better with feedback!

T1 IT2II I T3

s=3 s=6s=6

Feedback Example

0 5 10 15

0 5 10 15

T1={C=4,P=10,c=1}, T2={C=4,P=14,c=1}, T3={C=1,P=17,c=1}, IdleT={C=1,P=4,c=0}

100%75%50%25%

Actual Schedule without feedback100%75%50%25%

Actual Schedule with feedback (from the 1st hyperperiod) 480 485 490 495

Ca=1,s=3

f

f

f

t

t

t

T1 T2 T1IT1 IT2II I T3

100%75%50%25%

Maximal Schedule

Ca=1,s=3Ca=1,s=3